Spherical functions on a complex classical quantum group

Welleda Baldoni; Pierluigi Möseneder Frajria

Compositio Mathematica (1994)

  • Volume: 93, Issue: 2, page 113-128
  • ISSN: 0010-437X

How to cite

top

Baldoni, Welleda, and Möseneder Frajria, Pierluigi. "Spherical functions on a complex classical quantum group." Compositio Mathematica 93.2 (1994): 113-128. <http://eudml.org/doc/90316>.

@article{Baldoni1994,
author = {Baldoni, Welleda, Möseneder Frajria, Pierluigi},
journal = {Compositio Mathematica},
keywords = {quantum homogeneous space; spherical functions; Macdonald polynomials associated with root systems; complex quantum group; invariant elements},
language = {eng},
number = {2},
pages = {113-128},
publisher = {Kluwer Academic Publishers},
title = {Spherical functions on a complex classical quantum group},
url = {http://eudml.org/doc/90316},
volume = {93},
year = {1994},
}

TY - JOUR
AU - Baldoni, Welleda
AU - Möseneder Frajria, Pierluigi
TI - Spherical functions on a complex classical quantum group
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 93
IS - 2
SP - 113
EP - 128
LA - eng
KW - quantum homogeneous space; spherical functions; Macdonald polynomials associated with root systems; complex quantum group; invariant elements
UR - http://eudml.org/doc/90316
ER -

References

top
  1. 1 W.M. Baldoni and P. Möseneder Frajria, Spherical functions on SLq (2, C), (to appear). Zbl0814.17015
  2. 2 V.G. Drinfel'd, Quantum groups, Proceedings of the International Congress of Mathematicians, Berkeley, 1986, pp. 798-820. Zbl0667.16003MR934283
  3. 3 M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple, Ann. of Math.105 (1977), 107-120. Zbl0346.17011MR430005
  4. 4 G.J. Heckman, Lectures on Hypergeometric and Spherical Functions, Notes of the Lectures given at the European School of Group Theory, Marseille, July 1991. 
  5. 5 H. Jack, A class of symmetric polynomials with a parameter, R.S. Edinburgh69A (1970), 1-18. Zbl0198.04606MR289462
  6. 6 M. Jimbo, A q-difference analog of U(g) and the Yang-Baxter equation, Lett. Math. Phys.10 (1985), 63-69. Zbl0587.17004MR797001
  7. 7 M. Kashiwara, On Crystal bases of the q-analogue of universal enveloping algebras., Duke Math. J.63 (1991), 465-515. Zbl0739.17005MR1115118
  8. 8 T.H. Koornwinder, Continuous q-Legendre polynomials as spherical matrix elements of irreducible representations of the quantum SU(2) group, C.W.I. Quarterly2 (1989), 171-173. Zbl0677.33008
  9. 9 G. Lusztig, Quantum deformation of certain simple modules over enveloping algebras, Advances in Math.70 (1988), 237-249. Zbl0651.17007MR954661
  10. 10 I.G. Macdonald, Commuting differential operators and zonal spherical functions, Lecture Notes in Mathematics1271 (A. M. Cohen, W. H. Hesselink, W. L. J. van der Kalen, and J. R. Strooker, eds.), Springer-Verlag, Berlin- Heidelberg, New York, 1987, pp. 189-200. Zbl0629.43010MR911140
  11. 11 —, Orthogonal polynomials associated with root systems, preprint. 
  12. 12 —, Symmetric Functions and Hall Polynomials, 2nd edition (to appear). 
  13. 13 M. Noumi and K. Mimachi, Roger's q-ultraspherical polynomials on a quantum 2-sphere, Duke Math. J.63 (1991), 65-80. Zbl0780.33011MR1106938
  14. 14 P. Podles, Complex quantum groups and their real representations, Publ. RIMS28 (1992), 709-745. Zbl0809.17003MR1195996
  15. 15 N. Yu. Reshetikhin, L.A. Takhtajan, and L.D. Fadeev, Quantization of Lie groups and Lie algebras, Leningrad Math. J1 (1990), 193-225. Zbl0715.17015MR1015339
  16. 16 L.J. Rogers, Third memoir on the expansion of certain infinite products, Proc. London Math. Soc.25 (1895), 15-32. Zbl26.0289.01JFM26.0289.01
  17. 17 M. Rosso, Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys.117 (1988), 581-593. Zbl0651.17008MR953821
  18. 18 —, Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif, Duke Math. J.61 (1990), 11-40. Zbl0721.17013
  19. 19 Ya. S. Soibel'man, An algebra of functions on a compact quantum groups, Leningrade Math. J.2 (1991), 161-178. Zbl0718.46012MR1049910
  20. 20 S.L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys.111 (1987), 613-665. Zbl0627.58034MR901157

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.